Innovation dynamics and labor force restructuring with ...

International Business Review 26 (2017) 36–56

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International Business Review journal homepage: www.elsevier.com/locate/ibusrev

Innovation dynamics and labor force restructuring with asymmetrically developed national innovation systems Francisco J. Santos-Arteagaa,b , Debora Di Caprioc,d , Madjid Tavanae,f,* , Aidan O’Connorg a

School of Economics and Management, Free University of Bolzano, Bolzano, Italy Departamento de Economía Aplicada II Facultad de Económicas, Universidad Complutense de Madrid, Spain Department of Mathematics and Statistics, York University, Toronto M3J 1P3, Canada d Polo Tecnologico IISS G. Galilei, Via Cadorna 14, 39100 Bolzano, Italy e Business Systems and Analytics Department Lindback Distinguished Chair of Information Systems and Decision Sciences La Salle University, Philadelphia, PA 19141, USA f Business Information Systems Department, Faculty of Business Administration and Economics, University of Paderborn, D-33098 Paderborn, Germany g Département de Management, Systèmes et Stratégie, École Supérieure de Commerce et de Management, 11 rue de l’Ancienne Comédie, 86001 Poitiers, France b c

A R T I C L E I N F O

Article history: Received 3 May 2015 Received in revised form 22 April 2016 Accepted 8 May 2016 Available online 21 May 2016 JEL classification: O33 O15 O47 Keywords: Economic stagnation Technology assimilation Technological development Migration patterns National innovation system European single market

A B S T R A C T

The concept of National Innovation System (NIS) has gained a great deal of intellectual and practical attention over the past three decades. We present an endogenous growth model where the NIS of a country determines its accumulation of technological knowledge and the arrival rate of innovations depends on the distance from the technological frontier to the current technological development level (TDL) of the country. We show how, even within an ideal common market environment and despite the compensatory mechanism provided by migration and the advantage of backwardness enjoyed by the laggard countries, differences in TDLs among countries foster the economic stagnation of technological laggards. That is, the structural consequences derived from technological underdevelopment are persistent and not simply due to the depreciation of human capital, but to the absence of innovation incentives that follows. Numerical simulations and an empirical analysis are performed to illustrate the main results and relate them to the current European common market setting and the innovation policies of its members. ã 2016 Elsevier Ltd. All rights reserved.

1. Introduction 1.1. Motivation and intuition The economic literature has progressively recognized the fact that the assimilation of the most advanced technological capital by less developed countries constitutes a growth mechanism requiring important amounts of both physical and human capital investment (Aghion & Howitt, 1999, 2005; Howitt & MayerFoulkes, 2005; Sharif, 2006; Acemoglu, 2008; Borsi & Metiu, 2015).

* Corresponding author at: Business Systems and Analytics Department Lindback Distinguished Chair of Information Systems and Decision Sciences La Salle University, Philadelphia, PA 19141, USA. E-mail addresses: [email protected], [email protected] (F.J. Santos-Arteaga), [email protected] (D. Di Caprio), [email protected] , http://tavana.us/ (M. Tavana), [email protected] (A. O’Connor). http://dx.doi.org/10.1016/j.ibusrev.2016.05.005 0969-5931/ã 2016 Elsevier Ltd. All rights reserved.

Consequently, quality and level of education asymmetry, as well as, institutional and trade frictions constitute the main divergent forces highlighted in the literature. The importance of education in terms of human capital formation and accumulation, together with the institutional infrastructure of a country and its governance, have been empirically identified as determinants of innovation-induced growth by Varsakelis (2006), Giménez and Sanaú (2007), Fagerberg, Verspagen, and Caniels (1997), Chen, Hu, and Yang (2011) and Veugelers and Schweiger (2015). Moreover, the cumulative nature of technology is a widely recognized fact (Mukoyama, 2003), and the costs of learning a technology are known to be considerable (Engel & Kleine, 2015; Jovanovic, 1997). Thus, in an ideal common market setting without educational, institutional or trade barriers, all economic fluctuations should be caused by differences in technological development and assimilation levels among countries.

Innovation Dynamics and Labor Force Restructuring with Asymmetrically Developed National Innovation Systems Francisco J. Santos-Arteagaa,b of Economics and Management Free University of Bolzano, Bolzano, Italy E-mail: [email protected] aSchool

bDepartamento

de Economía Aplicada II Facultad de Económicas Universidad Complutense de Madrid, Spain E-mail: [email protected] Debora Di Caprioc,d cDepartment of Mathematics and Statistics York University Toronto, M3J 1P3, Canada E-mail: [email protected] dPolo

Tecnologico IISS G. Galilei Via Cadorna 14, 39100, Bolzano, Italy Madjid Tavanae,f,* Systems and Analytics Department Lindback Distinguished Chair of Information Systems and Decision Sciences La Salle University, Philadelphia, PA 19141, USA E-mail: [email protected] Web: http://tavana.us/ eBusiness

fBusiness

Information Systems Department Faculty of Business Administration and Economics University of Paderborn, D-33098 Paderborn, Germany Aidan O’Connorg gDépartement de Management, Systèmes et Stratégie École Supérieure de Commerce et de Management 11 rue de l’Ancienne Comédie, 86001 Poitiers, France E-mail: [email protected]

____________________________ *

Corresponding author at: Business Systems and Analytics Department, Lindback Distinguished Chair of Information Systems and Decision Sciences, La Salle University, Philadelphia, PA 19141, United States. Tel.: +1 215 951 1129; fax: +1 267 295 2854.

Innovation Dynamics and Labor Force Restructuring with Asymmetrically Developed National Innovation Systems Abstract The concept of National Innovation System (NIS) has gained a great deal of intellectual and practical attention over the past three decades. We present an endogenous growth model where the NIS of a country determines its accumulation of technological knowledge and the arrival rate of innovations depends on the distance from the technological frontier to the current technological development level (TDL) of the country. We show how, even within an ideal common market environment and despite the compensatory mechanism provided by migration and the advantage of backwardness enjoyed by the laggard countries, differences in TDLs among countries foster the economic stagnation of technological laggards. That is, the structural consequences derived from technological underdevelopment are persistent and not simply due to the depreciation of human capital, but to the absence of innovation incentives that follows. Numerical simulations and an empirical analysis are performed to illustrate the main results and relate them to the current European common market setting and the innovation policies of its members.

Keywords: Economic stagnation; Technology assimilation; Technological development; Migration patterns; National innovation system; European single market.

JEL Classification: O33; O15; O47.

1

1. Introduction 1.1. Motivation and intuition The economic literature has progressively recognized the fact that the assimilation of the most advanced technological capital by less developed countries constitutes a growth mechanism requiring important amounts of both physical and human capital investment (Aghion and Howitt, 1999, 2005; Howitt and Mayer-Foulkes, 2005; Sharif, 2006; Acemoglu, 2008; Borsi and Metiu, 2015). Consequently, quality and level of education asymmetry, as well as, institutional and trade frictions constitute the main divergent forces highlighted in the literature. The importance of education in terms of human capital formation and accumulation, together with the institutional infrastructure of a country and its governance, have been empirically identified as determinants of innovation-induced growth by Varsakelis (2006), Giménez and Salaú (2007), Fagerberg et al. (2007), Chen et al. (2011) and Veugelers and Schweiger (2015). Moreover, the cumulative nature of technology is a widely recognized fact (Mukoyama, 2003), and the costs of learning a technology are known to be considerable (Jovanovic, 1997; Engel and Kleine, 2015). Thus, in an ideal common market setting without educational, institutional or trade barriers, all economic fluctuations should be caused by differences in technological development and assimilation levels among countries. Consider, for example, a world economy composed by two types of countries each of which is defined by its National Innovation System (NIS). Assume that both countries produce the same good(s), technological innovations are transferred immediately and with negligible cost between them, and no trade, educational, institutional or demand frictions exist between the countries. All labor is skilled and allowed to move freely according to the wage received based on its marginal productivity. Countries only differ in their technological development level (TDL), which, at the same time, determines their ability to assimilate the knowledge implicit in any newly developed technology and generate further innovations (Ballot and Taymaz, 1997; Castellacci and Natera, 2015). Thus, countries will be distributed in two different groups, one composed by technological leaders and the other one by laggards. The above description corresponds to a textbook European common market subject exclusively to differences in TDLs across its members. We analyze the consequences derived from the corresponding technological adjustment process in terms of optimal labor allocation, migration patterns and technological evolution. We will identify the level of technological development of a country with that of its technological base. As illustrated by Furman et al. 2

(2002) and Castellacci and Natera (2013), the technological base [infrastructure] of a given country limits its ability to innovate and learn through assimilation if it does not develop simultaneously to the level of technological knowledge acquired by the workers. That is, human capital is redundant if it is not complemented by an adequate technological infrastructure. The lower the level of development of the technological infrastructure, the lower the factor productivity obtained from any new technology and the probability of generating innovations (Silva and Teixeira, 2011; Teixeira et al., 2014). As a consequence, the optimal allocation of labor across countries and their corresponding economic evolution would be directly determined by the level of development of their respective technological bases. However, despite the importance that innovation and the diffusion of technology have had for the European growth process through the 1980s, laggard countries failed to take advantage of the more advanced technology available due to a lack of their own R&D capabilities (Fagerberg et al., 1997). In this regard, the pervasive effects inherent in an underdeveloped NIS become evident when considering several indicators within the technology and innovation-related pillars composing the global competitiveness index (World Economic Forum, 2013). Table 1 presents the indicators selected from these technology-related pillars for the countries under analysis in the paper. The data represent the position of the corresponding country from a total of 148 composing the global competitiveness ranking. Insert Table 1 Here As illustrated in Table 1, the main constraints suffered by technological laggards (Greece, Italy, Portugal and Spain) are not the lack of skilled human capital or a limited access to the latest technologies available. Though slightly behind in both indicators, their situation is not considerably worse than that of the technological leaders (Denmark, Finland, Germany and Sweden). Indeed, as our empirical analysis will show, laggard countries are able to increase the resources dedicated to R&D activities when subject to a negative shock to their economies. On the other hand, the structural nature of the constraints suffered by these countries is reflected on: 

Their lack of capacity to innovate and retain talented human capital.



The inability of their firms to absorb technologies.

1.2. Contribution Given the intuition provided in the previous section, we build our model on two main features of the European economic system: 3



From a formal standpoint, Table 1 together with the literature surveyed imply that: o The integration of physical and human capital is required to generate persistent economic growth. o The development of the NIS is essential to determine the capacity of a country to assimilate technology and innovate.



From an empirical standpoint, the following behavior is observed across the European countries analyzed: o Technological leaders do not modify the intensity of their R&D when subject to shocks to their real economy. o Technological laggards react to shocks to their real economy by modifying the intensity of their R&D. However, these responses lack a persistent effect on their NISs. Our model accounts for the formal features described above and explains the

empirically observed behavior of the countries being analyzed. In particular, we illustrate how, even within a frictionless common market environment where technological innovations become immediately available to all countries, differences in TDLs constrain the incentives and the capacity of the laggards to innovate. Thus, as suggested by the literature on technological catch-up and absorptive capacities, differences in TDLs alone suffice to constrain the convergence process of the laggards (Hanusch and Pyka, 2009; López et al., 2011; Castellacci and Natera, 2016). However, the current paper goes beyond the fact that technological underdevelopment depreciates the skilled composition of the labor force and generates unemployment. As stated by the theoretical literature on brain drain and economic development (Docquier and Rapoport, 2012; Bosetti et al., 2015), migration processes reallocate skilled workers among the technologically developed countries allowing for a temporary relief within the laggard ones. We illustrate how, despite this compensatory mechanism and the advantage of backwardness enjoyed by the laggards, their incentives to innovate may also stagnate unless exogenous structural incentives are provided. The structural consequences derived from technological underdevelopment are therefore persistent and due not only to the depreciation of skilled unemployed human capital through time, but also to the long-run innovation disincentives that follow, which oppose the advantage of backwardness defined by Gerschenkron (1952). That is, the incentives generated by the economic system may be insufficient for the laggards to recover

4

technologically and converge. Thus, the design of science and innovation policy mixes should not only address the current brain drain taking place among technological laggards (Heitor et al., 2014), but also try to prevent their long-run economic stagnation (Borrás and Edquist, 2013). 1.3 On innovation and employment Innovation is quite a difficult concept to grasp and measure (Vivarelli, 2014b). Standard indicators such as research and development (R&D) and patents are not always fully available and are often inadequate to capture technological progress. In particular, small and medium enterprises generally perform innovation activities by acquiring capital and implementing its inherent technology into their production processes. Such an innovation strategy is referred to as embodied technological change. Empirical studies of the European Community have shown that R&D expenditures usually relate to product innovation, while innovative investments are associated with process innovation (Antonucci and Pianta, 2002; Parisi, Schiantarelli and Sembenelli, 2006). We consider both these approaches to innovation in our empirical analysis. More precisely, we will use the R&D intensity variables available from Eurostat and the Summary Innovation Index (SII) designed by the European Commission to measure the technological development and innovation capacities of countries. Formally, we introduce a variable,  , to simplify and condense the main ideas and concepts determining the TDL and the innovation capacity of a country. This variable will be used to define the total factor productivity (process) and the probability of introducing an innovation (product), which together determine the number of skilled workers that can be employed by the country. At the same time, introducing an innovation to the market will lead to both an increase in total factor productivity and an improvement in the technological base of the country. The effect of innovation on employment has been empirically shown to depend on whether the innovation introduced is in a product or in a process. See Vivarelli (2013) for a review of the literature on this topic. Harrison et al. (2014) used firm level data from Germany, France, UK, and Spain over the period 1998-2000 to illustrate the importance that the interaction between product and process innovation and the demand for products has for employment creation. They observed that process innovation causes a displacement of employment, while product innovation tends to generate employment. Bogliacino et al. (2013) reached a similar conclusion analyzing European business services over the period 1996-2007. However, they also noticed that the demand for new and old products can

5

mitigate the negative displacement effect. Van Roy et al. (2015) measured the labor-friendly nature of innovation within a set of 20.000 European patenting firms over the period 20032012. They observed that the positive impact of innovation is significant for firms in the high-tech manufacturing sector but not for firms in the low-tech manufacturing and service sectors. The efficiency of the compensation mechanism for the initial labor-saving impact of (process) innovation depends on the institutional environment of the country and on the sector specific values of parameters such as demand elasticity, degree of competition, capitallabor substitution, demand expectations, and so on (Pianta, 2005; Vivarelli, 2014b). We assume that all countries are identical in this respect, all endowed with an infinitely elastic demand and the same institutional environment. Our assumptions impose a positive relationship between innovation and employment, with a more developed technological base allowing a country to attract and employ a higher number of (skilled) workers. This leads to a self-reinforcing pattern in the behavior of countries, since a larger number of highly productive workers generates a higher amount of output and yields a higher innovation probability. In this regard, the growth mechanism considered in this paper differs from the standard one employed by growth theorists, which relies on capital accumulation as the mechanism leading to productivity growth and economic development (Greenwood, Hercowitz, and Krusell, 1997; Wilson, 2009). In our setting, knowledge will be assumed to be embodied in the technological base of a country and accumulate as its NIS develops. Finally, we also assume that the efficient implementation of the available technology requires suitable skills among the labor force, i.e. skilled-biased technological change. Consequently, the lack of skilled labor limits the adoption and diffusion of new technology, defining a human resource constraint that restricts the production of a country and its capacity to innovate (Amendola and Gaffard, 1988; Murphy and Topel, 2016; Pargianas, 2016). Note, that at the same time, we do not consider the budgetary burdens derived from a relative increment in the number of unskilled or unemployed workers within the laggard countries. The paper proceeds as follows. Section 2 introduces the model and derives analytically the optimal behavior of countries. Section 3 analyzes numerically the main consequences of the model for convergence via wage differentials. Section 4 verifies empirically the formal results obtained in the previous sections. Section 5 studies the resulting policy implications and the consequences for the Europe 2020 strategy. Section 6 presents the main conclusions derived from the paper. Formal proofs are relegated to the 6

appendix. 2. The basic model 2.1. Assumptions Consider, without loss of generality, a common market area consisting of two countries and one industrial sector (NIS) per country composed by a finite number of M firms operating within it. We assume that the goods produced in each country are identical, that is, both countries have a unique overlapping sector. The main results obtained hold if a continuum of industrial sectors is considered. In this case, differences between countries would be based on the relative development of their NISs (Lundvall, 2007; Hardeman et al., 2015). Similarly, if a larger number of countries is assumed to compose the common market area, they could be classified in different convergence groups according to their TDLs, an exercise already validated empirically by Filippetti and Archibugi (2011) for the Euro-27 group. In addition, identical unitary prices are assumed in both countries for the most technologically advanced good being produced. The exchange rate is fixed within the area and is assumed to be equal to one. There are initially n  workers per firm in each country. The labor force is composed exclusively by skilled workers, who are used in manufacturing and innovation activities. That is, the initial endowments of human capital are identical in both countries. A differentiated distributive approach distinguishing between unskilled manufacturing and skilled innovative labor is presented in López et al. (2011). We are however interested here in the divergent effects derived from the continuously evolving technological race that takes place between countries through time absent labor allocation considerations. Thus, human capital formation processes are not accounted for and identical education systems are assumed in both countries, a far from mild assumption when the European market area is considered (European Commission, 2013). It should be noted that relaxing this assumption would worsen the innovation capabilities of the laggards. If labor is used in manufacturing activities, the quantity of manufactured output produced is limited by the relative TDL of the country. This variable reflects the distance existing between two countries within a particular technological paradigm and it is described as follows:  

r , where * accounts for the level of development of the technological base * 

necessary to generate the latest productivity improving innovation (i.e. the technological frontier), while r stands for the level of development achieved by the technological base of 7

the country. At the same time, when labor is used in innovative activities it increases the probability of innovating and achieving a higher TDL, i.e. of improving the technological base of the country. The innovation probability of a country as well as the productivity of its labor will both be determined by  , a fundamental point to which we will return in the next section. We assume time to be continuous and measured by discrete innovations. That is, one unit of time corresponds to the time interval required for the next innovation to appear. If, in particular, two innovations take place simultaneously, continuity allows separating them in two different units of time (Aghion and Howitt, 1992). At a given point in time, one of the firms within a given country develops and introduces an innovation in the market while the remaining ones behave as manufacturers. We will refer to the former one as the innovator firm (IF) and to the latter ones as the manufacturing firms (MFs). The country whose industry accounts for the latest innovation will be called innovator country. Differently from the theoretical literature on quality ladders (Grossman and Helpman, 1991), we assume that all firms in both countries have immediate access to the most advanced production technology. A common development strategy is assumed to be followed by the whole [common] market area so that no patent or technological monopoly constitutes an impediment for convergence between countries. Thus, innovations give the innovator a factor productivity advantage over the rest of the firms in both countries. As a result, all firms will charge the same quality adjusted price for the most technologically advanced good being produced. We assume that innovation incentives are provided by infinitely elastic demand functions absorbing the whole production of the good per period of time in each country. This assumption, together with the fixed unitary exchange rate and the identical quality adjusted prices, prevent both countries from trading in goods. It should be emphasized that relaxing any of the assumptions described above would have an immediate effect on the innovation incentives of the laggard countries, yielding a downward shift of their corresponding equilibrium wage functions. This would restrain the prompt response of laggards to decrements in the relative development of their NIS and increase the lower limit level of  at which the stagnant trap starts. The production function of a MF located in a technological laggard country is given by

Ysm  A1 K  n1 ,

(1) 8

where K refers to the physical capital used in production while A corresponds to the productivity of the technology, which will be assumed identical to the productivity frontier A* at all points in time for both countries. Note that the most productive technology can

only be exploited up to the limit imposed by the TDL of the country. That is, all firms in both countries are able to produce the most technologically advanced good and have access to the same frontier technology, but their total factor productivity differs depending on the value of

 achieved by the country where they are located. The production function of an IF in its industrial sector is given by

Ysn  2 A1 K  n1 ,

(2)

where   1 , and   1. Developing a leading technological innovation allows the IF to increment its productivity over that of the previous industry leader by a factor of  . That is, total factor productivity grows at a constant rate of (  1) per unit of time. Also, being a technological leader implies that the value of  within the corresponding industrial sector must be equal to one. In order to account for geographical knowledge and technology spillovers, we will assume that the production function of the MFs located within the innovator country is given by

Ysm   A1 K  n1 ,

1    .

(3)

MFs located in the innovator country benefit from being geographically close to the IF, which allows for direct information spillovers that increase their factor productivity (Cohen and Levinthal, 1989; Singh, 2007; Livanis and Lamin, 2016). This location advantage constitutes the only friction in favor of the innovator country explicitly introduced within the current environment. All workers receive the same wage within a country, wm in technological laggards and wn in the innovator country, independently of their activity. Since the price of the most technologically developed good being produced is identical in both countries, all wages will be directly comparable in real terms. That is, divergences in real wages will be caused by productivity frictions derived from differences in  values between countries. We omit the effects that monetary policies designed to distort prices may have on the wage distribution between countries. Governments are therefore limited in their ability to use these instruments and compete exclusively in terms of TDLs.

9

2.2. Optimizing countries Countries face the intertemporal problem of maximizing the expected flow of profits obtained from their firms while being limited by their TDL. The expected profit function corresponding to a technological laggard country is given by 

(4)

(t )  E  e  [ t ] (n |  ) d , t

where

 (n |  )   A1 K  n1  wmn ,

(5)

 represents the rate of time preference for any given firm, assumed identical both among firms and between countries, and wm stands for the wage paid to the skilled labor. Note that the definition of  (n | ) provides a simplified version of the proportional composition of the industrial sectors under consideration and will be also used for the profit function of the innovator country. That is, the factor productivity of the industrial sector of the innovator country is given by

1 M 1   , which should lead to the following M M

expression for its profit function:   M  1  1  1    A K n  wn n . M M  

(6)

 (n |  )  

This equation describes a unique IF whose productivity (  ) is higher than the productivity (  ) of the remaining M  1 MFs within the country. However, to simplify this equation we define the profit function of the innovator country as follows

 (n |  )  A1 K  n1  wn n .

(6')

A similar simplification is imposed when defining the stochastic evolution of the TDL of countries. Innovations within the industrial sectors of a country are governed by a Poisson process

whose

arrival

rates

are

respectively

defined

by

 ( , n)   n

and

( ,n)    (1   )  n . That is, the technological distance between countries and the number of skilled workers affect their innovation probabilities. Note that we have endowed laggards with a basic TDL,  , on which their current  can build to prevent complete stagnation at low levels of development. The importance of  as a mechanism of direct technology transfer will be highlighted in the numerical simulations. As illustrated in the following section, these functional forms decrease the converging capabilities of technological laggards. 10

Note that the workers located in the innovator country have access to a more developed technological infrastructure than those located within the laggard country. As a result, knowledge and human capital accumulate and spread faster in the innovator country, leading to a higher innovation probability. See Gupta and Chakraborty (2006) for a related formal setting. The stochastic evolution of the TDL achieved by a country per innovation unit of time is determined by its current value and the Poisson process defining the innovation arrival rate. The increase in the TDL of a laggard country if an innovation takes place among any of its firms equals  2  M  1 M  1  d m        dz , M M M M  

(7)

with the arrival rate of the corresponding Poisson process z determined by ( , n) . Similarly, the increase in the TDL of an innovator country if an innovation takes place among any of its firms equals  2   d n    dz . M M   

(8)

The technological growth function defined within the laggard industry consists of an increase from an initial  productivity level in all M firms to a resulting  2 level in one of the firms and a level of  in all the M  1 remaining ones. In the same way, an innovator country would obtain an increment in the productivity of one of its firms from a level of  to a level of  2 , with all of its M  1 remaining firms stabilized at  . Equations (5)-(8) and the Poisson arrival rates illustrate how the model allows for the index variable  to account for all the technological differences existing between countries. That is, we are implicitly assuming that an innovation develops the technological infrastructure of its corresponding industrial sector but that such an advantage does not necessarily generalize to the whole country. In this regard, Equations (7) and (8) could be redefined in terms of industrial sectors, instead of firms within a sector, to highlight this restriction. Such a constraint emphasizes the importance that the whole technological infrastructure of a country (i.e. its NIS) has for its economic development (Furman et al., 2002; Bartels et al., 2012). Indeed, a country may master technologically a particular sector but lack the required infrastructure at the country level to evolve technologically and grow, a case represented by 11

Cuba and its highly sophisticated biotechnological sector (Thorsteinsdóttir et al., 2004; Nature, 2009). Similarly, individual firms within laggard countries may master innovation in their corresponding sectors while the country remains technologically underdeveloped (Forbes and Wield, 2008). In other words, increasing the number of sectors considered would not modify the main results obtained. Furthermore, the skilled labor force must interact with the technological infrastructure of the country to generate economic growth. That is, countries can be endowed with a highly qualified labor force but lack the infrastructure to develop technologically and generate innovations. Two significant examples where the lack of coordination between human capital and their corresponding infrastructures has constrained economic growth are those of India and Russia. The former has a large (publicly funded) technological infrastructure and a considerable education base, but is constrained by a fragmented innovation environment exacerbated by bureaucratic inefficiencies (Herstatt et al., 2008; Abhyankar, 2014). The latter is characterized by the very high quality of its research but is limited in the absorption capacity of innovations and the generation of significant technology-based economic growth (Williams, 2011). Due to the comparative nature of this study, we consider the innovator country as the reference point to which laggard countries must converge. Thus, we simplify the equations defining the stochastic evolution of  as we did with the profit function of the innovator country. That is, we treat the evolution of each sector as that of a unique firm. Note that this modification leaves the main results qualitatively unaffected while simplifying the presentation considerably. The stochastic differential equation defining the evolution of  within the laggard country reads as follows:





  (n |  )  2 d m    dt     dz ,  ( n |  )  

(9)

while that defining the evolution of  within the innovator country is given by





d n  1dt  2  1 dz .

(10)

All profits have been assumed to be invested by each country in the improvement of their relative TDLs, with the laggard country being able to invest a smaller amount than the innovator one ceteris paribus. Note the larger improvement in TDL derived from an innovation by the laggards relative to that of the leader/innovator. That is, it is possible for the laggards to catch-up with the innovator though the probability of doing so is determined 12

by  ( , n) . The model has been designed to represent different countries within a common market area that share sufficient similarities to allow for relatively frictionless migration flows between them. Thus, even though n is initially identical in each country, relative changes would take place if a laggard country cannot provide the wage incentives required to maintain its skilled labor force. The absence of trade between countries implies that the migration patterns act as a compensatory force to equate their w levels. 2.2.1. Optimality The continuous flow of technology has a direct effect on the optimal behavior of countries, which must maximize all the output obtained from their skilled labor given their relative TDL and the probability that any of their firms develops the next innovation. The Bellman equation defining the intertemporal optimization problem of a laggard country is given by1 

   (n |  )   ( , n) [V ( 2 )  V ( )] ,    (n |  )  

V m ( )  max  (n |  )  V ( )  n



(11)

while that of the innovator country is

V n ( )  max  (n |  )  V ( )  ( ,n) [V (2 )  V (1)]  . n



(12)



Both equations allow for a direct comparison between the outputs generated through manufacturing and innovation activities, respectively. Manufacturing increases the current profits of countries (i.e.  (n |  ) for laggard countries and  (n |  ) for innovator ones), and leads to a deterministic increase in  , whose marginal value is denoted by V ( ) . Clearly, the marginal value effect of manufacturing on  must account for the corresponding profits obtained and invested by the firms of the innovator country. At the same time, the expected output derived from introducing an innovation is computed multiplying the arrival rate defined by the corresponding Poisson process, ( , n) and ( , n) , by the respective value increase determined by the changes in  , [V (2 )  V ( )] and [V (2 )  V (1)] . Countries must therefore find a balance between their (short run) manufacturing incentives and their (long run) expected innovation profits. See Arcalean et al. (2012) for a related trade-off setting. After some algebra, we obtain the following first order condition for laggard countries 1

Refer to the Appendix section at the end of the paper for the derivation of both these Bellman equations.

13

w*m 

(13)

(  (1   ) )[V ( 2 )  V ( )] , V ( )   1     (n |  )   

and the corresponding one for the innovator country

w*n   [V (2 )  V (1)] ,

(14)

with

w*m  wm  (1   ) A1 K  n ,

w*n  wn  (1   ) A1 K  n .

(15)

The first order conditions are expressed as equilibrium equations describing the wage differentials between countries. The optimal wage paid to skilled workers, w*i , with i  m, n , is therefore determined by the value gain differentials [V (2 )  V ()] existing between both countries and the marginal value change generated by technological development in laggard countries, V ( ) . In other words, the first order conditions provide a rule relating the optimal allocation of skilled labor between countries to the relative values of  (and  ). Absent cultural differences-based frictions, which is a far from innocuous assumption to be made regarding the European Union and its member states (De Simone and Manchin, 2012), migration patterns can be assumed to follow real wage differentials between countries. That is, workers may be assumed to maximize their total consumption, c , given the unique set of unitary prices and a budget constrain such that c  w , where w stands for the wage received by the worker. In this case, optimal wage dynamics depend on the relative differences existing between [V (2 )  V (1)] and

[V ( 2 )  V ( )] . In particular, the model V ( )   1    ( n |  )  

will give place to convergent dynamical patterns if  (  (1   ) )  [V ( 2 )  V ( )] V ( 2 )  V (1)   ,     1  V ( )      (n |  ) 

(16)

while divergent dynamical patterns may be generated reversing the above inequality. Divergences are also exacerbated if the technological distance between countries leads the wage paid to skilled workers within the innovator country to be higher than the one paid by the laggards. That is, if technological laggards were forced to hire a lower number of workers in order to increase their relative productivity and, therefore, their wages, then the

14

corresponding innovation probability ( , n) would also decrease. The numerical section shows that as the degree of concavity defining the value function increases, the set of  values leading to the technological stagnation of the laggards tends to widen. 3. Results 3.1. Basic intuition The implications of the relative TDL for the wage differentials and optimal distribution of labor between the innovator and the laggard are determined by the first order conditions defined by Equations (13) and (14). In other words, the technological evolution of laggard countries will be determined by the value function form defining the right hand sides of both these equilibrium equations. In our model, wage differentials can be used by laggard countries to attract skilled labor in order to compensate for their lower TDL. At the same time, the number of skilled workers determines the investment in R&D activities through the innovation probability. Thus, the compensation mechanism implemented by the government via higher wages does not only aim at attracting skilled labor but also indicates an increase of the investment in R&D activities (and technological infrastructure). Our model can be generalized to account explicitly for this difference, at the cost of incrementing the number of equilibrium equations and increasing the complexity of the resulting mathematical structure. However, the main results would not be qualitatively modified and the intuition derived from such a model can also be described using the simpler one presented in the current paper. Note that, in order for the system to be in equilibrium, wages in both countries must be identical, that is, wn  wm . The resulting equilibrium dynamics are easily understood after observing that whenever w*n  w*m , then wn  wm ceteris paribus, generating a divergent pattern. Assume, for example, that w*n  w*m . Then, in order to pay its workers the same wage as the innovator country, i.e. for wm to be equal to wn , the laggard country must unilaterally decrease the number of skilled workers hired, nm . By doing so, both its innovation probability, ( , n) , and output level decrease relative to those of the innovator country. A similar but milder process, due to the fact that    , applies to the nn workers of the innovator country when w*n  w*m . Note, however, that this latter advantage in wages does not guarantee the technological convergence of the laggard, since this country remains constrained by a  value that decreases progressively as the technological gap between 15

countries widens through time. 3.2. Numerical simulations Equations (13) and (14) can be interpreted as the wage incentives available from the respective countries so that they may grow through technological innovations. If, on the right hand side, the numerator is larger than the denominator, then the wages offered by the corresponding country increase due to the relatively high expected rewards obtained from an innovation. If the numerator is smaller than the denominator, then the incentives to grow technologically decrease as the resulting catching up process does not provide a sufficient motivation in terms of innovation rewards. Consider the case of a laggard country whose TDL falls below that of the current innovator. The existing technological gap implies that [V (2 )  V ( )]  [V (2 )  V (1)] , a value difference providing convergence incentives due to the advantage of backwardness exhibited by the laggard country. Indeed, the numerators on the right hand sides of Equations (13) and (14) represent the expected [via marginal probability increments] gain from using an additional unit of skilled labor in innovative activities. If, at the same time, the denominator of w*m decreases when  does, an increasing amount of labor resources could be absorbed by the laggard country due to the resulting relative increment in its wage level. Note that

V ( )

 (n |  )

represents the productivity effects that result from manufacturing

labor activities. As the reference profit value of the innovator country  (n |  ) increases, so does the reward derived from increasing the productivity of manufacturing, which leads to higher wages being offered by the laggard. If V ( ) increases, then the gain in manufacturing productivity becomes relatively large compared to  (n |  ) . Thus, whenever

V ( )

 (n |  )

increases (decreases) laggard wages decrease (increase), as relatively low (high) reference profits are attainable through large (small) productivity increments. Therefore, the dynamic evolution of the system depends on the value function form assumed in Equations (13) and (14). We concentrate on the concave value function scenario, which seems the most plausible one given the current situation of the technological laggards within the European economic area in terms of NIS (Filippetti and Archibugi, 2011; Di Caprio et al., 2015). A concave value function leads laggard countries to stagnation if V ( ) exhibits a sufficiently large increase when  approaches zero. As a consequence, countries 16

with relatively low  values would hire an increasingly lower proportion of skilled labor. The numerical wage function simulated to represent the convergence (and divergence) intervals defined by Equation (16) assumes V (2 )  V (1)  1 ,   1.1 and  (n |  )  20 . Note that [V (2 )  V ( )]  1 whenever   1 . Thus, the different patterns obtained from varying the concavity of the value functions can be compared among themselves and relative to

V (2 )  V (1)  1 as  decreases. It should be emphasized that, while conditioning quantitatively the results obtained, the numerical values chosen do not affect the qualitative intuition derived from the model. Figure 1 shows that decrements in the reference profit value obtainable by the laggards may lead to reversals in the dynamical patterns exhibited by wages. The simulated profit functions have been obtained changing the denominator of w*m in Equation (13) from

1

V ( ) 20

to 1 

V ( ) 10

, with V ( )   1 1   ,   2 and   0.5 . Insert Figure 1 Here

The upper and lower areas defined with respect to [V (2 )  V (1)]  1 within Figures 1, 2 and 3 represent the corresponding convergent and divergent equilibrium sections described above. Moreover, the simulations introduced in Figures 2 and 3 illustrate how as the degree of concavity of the laggard value function increases (i.e. as the marginal productivity gain derived from  increases) the interval of  values leading to their technological stagnation tends to widen. In Figure 2 we compare w*m in Equation (13) with [V (2 )  V (1)] =1 when 1

V ( )   2 , V ( )   4 , V ( )  ln  , and V ( )  1

 1 with   2 . The curvature, i.e. the 1

coefficient of relative risk aversion, of these value functions is equal to 0.5, 0.75, 1 and 2, respectively. Note the lack of capacity of the laggards to converge when   0.5 and 1

V ( )   2 or V ( )   4 . That is, the innovation probability of the laggards when these value 1

functions are considered does not suffice to generate convergence for any value of  . Thus, in Figure 3 we increase the basic endowment of technological development of the laggards to

  0.9 . The resulting increment in the probability of innovation suffices to foster the convergence capacity of the laggards, which is lower for the more concave value function. Insert Figures 2 and 3 Here 17

Figures 4 and 5 compare the effects that different value functions have on the width of the stagnant intervals. More precisely, these figures illustrate how the innovation incentives derived from the increments in technological development value differentials are compensated by the marginal productivity effects resulting from the curvature of the value function. Note, in particular, the larger innovation value increments defined by the isoelastic function relative to the natural logarithm one in Figure 4, where the value functions 1

V ( )   2 , V ( )   4 , V ( )  ln  , and V ( )  1

 1 are represented on the domain [0, 1]. 1

Insert Figure 4 Here However, when determining the laggard wages defined in Figures 2 and 3, these increments in the value gain derived from an innovation are weighted downwards by the effect of the marginal increment in the productivity of manufacturing. Figure 5 illustrates both effects at work for the isoelastic value function. In the same way, Figures 3 and 4 show that the lower technological value gains achieved for   [0; 1] together with a higher 1

curvature of the value function lead to a larger stagnant interval when V ( ) shifts from  2 to 1

4. Insert Figure 5 Here Clearly, any increment in the technological value gains achieved by the innovator country would widen the stagnant interval faced by the laggards. Migration flows equate wage levels between countries and stabilize the system as further innovations are developed. As illustrated in Figures 1 to 3, when  approaches zero,

nm decreases in the laggard, whose innovation probability, ( , n) , falls as the innovator country widens the technological gap. Absent migration, laggards would be able to keep a constant nm value while paying a decreasing wage to their workers as the divergent process takes place. However, keeping a constant amount of skilled labor does not necessarily prevent stagnation since the innovator country, which has an identical labor endowment, maintains a consistently higher innovation probability through time. 4. Empirical analysis 4.1. Descriptive statistics The main structural properties defining the European common market framework are reflected in our model. To validate this claim, we analyze the behavior of the variables

18

presented in Table 2, which will be used to determine the differences between the laggards and the leaders in terms of their economic performance and TDLs. We build a panel of data using the Eurostat series of these variables over the 2000-2013 period. The data retrieved from Eurostat for the whole set of countries under analysis is summarized in the online appendix. Insert Table 2 Here The variables presented in Table 2 have been selected to verify the main dynamical patterns that result from the theoretical model introduced in the previous sections. ΔGDP, ΔAVGDP and Prod describe the evolution of the manufacturing (production) process within the economic system. These variables are mainly determined by the TDL of the corresponding NISs (Lundvall, 2007) and reflect the structural capacity of countries to generate the output required to foster economic growth. Note, that while ΔGDP constitutes a proxy for the evolution of the national economic conditions, ΔAVGDP provides a measure of dispersion describing the convergent or divergent process taking place among the selected countries. The second set of variables, Emig and LF, reflects the population adjustment process taking place through migratory flows. Given the evolution of these variables, we can observe how the labor market assimilates and adjusts to the real shocks affecting the economic system. However, as illustrated in our model, these flows are only part of the adjustment process. The structural adjustment process takes mainly place through the interaction of the skilled labor force and the technological base of the country, whose level of development determines the innovation capacity of the country. This latter trend is captured by the last four variables, i.e. the number of workers dedicated to R&D activities, their proportion of the labor force, the expenditure on R&D activities and the summary innovation index. Given the results derived from our model and the dynamic trends observed in Figures 10 and 11 for both the European leader and laggard countries, we will assume that emigration flows are mainly determined by the economic conditions of the sending country (Gropas and Triandafyllidou, 2014). That is, when subject to real economic shocks such as the crisis of 2008, technologically developed countries endowed with a superior NIS do not experience an increasing flow of emigrants, while technological laggards do. Some technical remarks regarding the choice of the total number of emigrants as the variable measuring the emigration process follow. Note that we have not considered the standard labor force age group (15-64) within the total number of emigrants since the 19

corresponding data matrix has multiple values omitted for the countries under analysis. A similar observation applies to immigration data. In particular, there are substantial lacunae in the data when trying to identify either the immigrants within the 15-64 age group or those who are citizens from other European countries (refer to the Eurostat matrix [migr_imm1ctz]). Given this latter constraint and the fact that immigrants arrive from multiple sending countries and are not always migrating for purely economic reasons (Morano-Foadi and Malena, 2012), we have decided to concentrate on emigration flows. Furthermore, in our model immigrants constitute the complement of emigrants, i.e. the workers leaving from a country are those received by the other country. The average values of the main indicators over the period 2000-2013 are described in Table 3, where the moderate innovators [laggards] and the innovation leaders are represented in red and black characters, respectively.2 The differences between technological leaders and laggards are evident when considering the main structural variables. Note, for example, how annual GDP variations differ substantially from the average growth dispersion illustrated by the variable ΔAVGDP. Among the technological leaders, this difference is particularly relevant for Denmark, whose increment in GDP relative to the average level is not reflected in ΔGDP. Given our formal results, we could state that the substantial differences in labour productivity between both groups of countries together with the lower intensity of R&D activities and investment among the laggards lead to the lower development of their NISs reflected by the respective SII values. Insert Table 3 Here The evolution of Germany and Spain deserves particular attention, since it reflects the different trends followed by leaders and laggards within the European area and provides intuition for the statistical analysis performed in the next section. The values of the main structural indicators for both countries over the entire time period considered are presented in Tables 4 and 5, respectively. Insert Tables 4 and 5 Here Figures 6 and 7 describe the evolution of the main structural variables of both countries. The behaviour of ΔGDP illustrates how Germany grows at a higher rate than Spain since 2006, with the difference between both countries decreasing in the latter years.

2

This classification follows from the Innovation Union Scoreboard provided by the European Commission, which is available at http://ec.europa.eu/growth/industry/innovation/facts-figures/scoreboards/index_en.htm?nl_id=1041.

20

However, the dispersion exhibited by ΔAVGDP indicates a divergent process, particularly since the beginning of the 2008 crisis. The absence of a convergent trend is also illustrated by the productivity of both countries, which has increased over the years by five percentage points, while keeping a constant distance of ten points between them. The lower capacity of the laggards to react to structural shocks will also arise in the statistical correlation analysis, with laggards being affected by shocks to GDP growth while leaders react to average growth dispersion differentials. Insert Figure 6 Here The emigration flows present an even more drastic picture consisting of a steady substantial growth in Spain since 2005 and a considerable decrease in Germany after the crisis. The convergence between both countries in terms of R&D personnel as a percentage of the labor force also slows down in 2008 and reverses its trend afterwards. Overall, Figures 6 and 7 show that the crisis accentuates the structural weaknesses of the laggard relative to the leader, leading to the subsequent emigration process and to a lower dedication of skilled labor to R&D activities. Insert Figure 7 Here 4.2. Correlation analysis The analysis of the correlation between the structural variables considered validates the main results obtained from the formal model. We first compute the correlation between variables for all countries. Then, a second analysis differentiating between technological leaders and laggards is performed. As intuition suggests, the results will differ considerably between both types of countries, while following from those presented in Figures 1 to 5. Insert Table 6 Here Table 6 presents the correlations obtained when both leaders and laggards are included in the analysis. The absence of a relationship between the main structural variables and the annual growth of GDP may seem a bit surprising. However, a considerable positive relation is obtained when the dispersion based on the average GDP of all countries is considered. An increment in the dispersion between both groups of countries reflects the divergent process taking place among the countries that compose them. Note how emigration relates positively to the productivity of the labor force and to the average growth dispersion among countries, indicating an increment in the number of emigrants together with an increase in labor productivity as the GDP of a country grows with respect to the average. We elaborate further on this relation through this section, 21

differentiating in terms of the TDL of countries. In summary, the structural variables are highly correlated among themselves and relate positively to increments in GDP dispersion and productivity, both of which are accompanied by an increase in the size of the emigrant population. This description matches better the behavior of the technologically developed countries in our model than that of the laggards (see Figures 2 and 3). The intuition justifying this claim is reinforced by the absence of a relation between negative shocks to the economic system and the incentives of countries to adjusts (i.e. increase) the resources dedicated to their innovation systems. Recovering from the shock does not only allow the country to regain its previous production capacity, but also to expand it, thereby increasing the value gain derived from an innovation. That is, given the results of our model, laggards should dedicate a larger proportion of their resources to develop their NISs both as the technological distance with respect to the leaders widens (i.e. as  decreases) and as the value gain derived from an innovation increases for any given  (i.e. as w*m shifts upwards). A persistent negative shock to the real economy should therefore be compensated by an increase in the resources allocated to R&D activities, though this response does not necessarily lead to the development of the NIS of the laggards. In order to provide additional intuition, we have illustrated the relation between ΔGDP and emigration flows (Emig/LF) for all countries in Figure 8 (a), where a clear pattern cannot be seen to emerge. However, when considering only the technological laggards in Figure 8 (b), negative shocks to the economy are met with increments in the emigration flow. At the same time, the positive relation between ΔAVGDP and emigration flows for all countries is illustrated in Figure 9 (a) and reinforced in Figure 9 (b), which describes the stronger relation arising when the technological leaders are considered. Insert Figures 8 and 9 Here Therefore, we perform a statistical correlation analysis for each group of countries separately. Consider first the technological leaders. Insert Table 7 Here The results displayed in Table 7 illustrate the absence of a significant relation between the structural variables and the annual GDP growth among technological leaders. However, the structural variables and the emigration flows relate significantly to the average GDP dispersion variable. In other words, ΔAVGDP describes the structural-based growth of these countries. Note how emigration correlates positively with productivity and the relative 22

growth of the economy. In this regard, the increment in productivity may be due to the increase in emigration or to the high TDL of the countries. At the same time, the resources devoted to innovation activities, i.e. the proportion of R&D personnel in the labor force and the expenditure in R&D activities, decrease as emigration increases. This is the type of behavior described in our model for countries with a high  and whose value functions do not provide a substantial incentive for the development of innovations (see Figures 2 and 3). Technologically developed countries have the capacity to innovate but the expected value gain is not as substantial as it would be for a laggard, whose main constraint is given by its limited capacity to innovate in terms of innovation probability. Thus, leaders may experience an increase in emigration and a decrease in the resources dedicated to R&D activities while growing due to their developed NISs. Insert Table 8 Here Consider now the technological laggards described in Table 8. As in the case of the leaders, ΔAVGDP describes the structural-based growth of the country. However, laggard countries also react to shocks to ΔGDP. In this case, negative real shocks are met with increments in the resources dedicated to R&D activities and an increase in the emigration flow. That is, the economic system of the laggards is more sensitive to shocks to the real economy, with the labor market and the R&D intensity reacting to smooth them. This adjustment mechanism, consisting of an increment in the resources devoted to R&D activities in order to compensate - to some extent - for the divergent effects of a negative GDP shock, can be observed for the lower levels of  in Figures 2 and 3. That is, as the potential gains derived from an innovation increase [via a decrease in  or a direct increase in the value gain from innovating], so do the incentives of the laggards to increment their R&D activities. As already stated, the equilibrium wages have two related interpretations in our model. One as incentives to prevent skilled emigration and the other as investment in innovation-related resources through the skilled labor employed by the country. Thus, by increasing the wage paid above the one of the leaders, the laggards aim both at preventing migration and increasing their innovation probability through nm . As shown by the correlations, despite the efforts of the laggards to prevent the differences between NISs from widening, emigrant flows would result from negative shocks to the real economy. However, despite the considerable brain drain process described in the literature (Gropas and Triandafyllidou, 2014), either a majority of the emigrants leaving the laggard countries could be considered to be unskilled ones or the labor force is sufficiently skilled to compensate for 23

the brain drain process. Thus, increments in the emigration flow respond to changes in GDP in the same manner the country attempts to compensate for the decrease in GDP by increasing its R&D resources. Finally, note how the development of the NIS (SII) among technological laggards relates significantly to ΔAVGDP, productivity, and the intensity of R&D activities, but not to emigration. That is, the development of the NIS of a country requires considerable structural investments in R&D activities, with emigration acting as a compensatory mechanism relating to real but not to structural shocks to the economy. Once established, as in the case of the technological leaders, the NIS evolves together with ΔAVGDP and the funds allocated to R&D activities. 5. Policy implications 5.1. Structural constraints at work The model introduced in the paper has formally proven that technological underdevelopment may pervade within technological laggards in [long-term] structural terms despite the compensatory migration effect at work. This is the type of dynamic scenario described by the Eurostat and Innovation Union Scoreboard-based Figures 10 and 11. Insert Figure 10 Here These figures illustrate the different trajectories followed by the moderate innovators [laggards], including Spain (SP), Greece (GR), Italy (IT) and Portugal (PT), and the innovation leaders, consisting of Germany (DE), Denmark (DK), Finland (FI) and Sweden (SE). Figure 10 illustrates the total number of long-term emigrants as a percentage of the labor force (Em/LF) for all the countries during approximately the last fifteen years. Figure 11 provides the SII, which has been used as a proxy for the quality and strength of the NIS of each country. Note that, in the current paper, we have represented this concept using the variable  . Insert Figure 11 Here Consider the trends observed in the emigration patterns within both sets of countries. The increment in [long-term] emigration observed among the laggards, particularly Greece and Spain in the years immediately following the 2008 crisis, contrasts with the containment observed among the technological leaders, with Denmark and Finland experiencing decrements in their corresponding number of emigrants. However, the main decrease in the emigration flow is the one experienced by Germany, which, due to its considerable size in economic and population terms, remains as the main European technological reference 24

country. At the same time, the data illustrates how this compensatory migration mechanism lacks a structural counterpart in the development of the NISs of the laggards, which remain consistently below the European average, while countries like Denmark and Germany have consistently developed them after 2008. In other words, the European economy does not converge in structural technological terms. We could complement Figures 10 and 11 by illustrating the net financial assets of the corresponding group of countries, with the government debt of all technological laggards accounting for more than 100% of their GDPs. Despite the expected increment in the innovative activity of the laggards, due to their advantage of backwardness and the inflow of foreign funds, we observe a progressive stagnation in the development of their NISs relative to those of the technological leaders. Thus, in addition to the synergies lost due to the modification of the labor force (Herrmann and Peine, 2011), the reallocation of labor through migration hides a perverse structural problem in the laggard countries. As Table 1 illustrated in the introduction, laggard countries endowed with a considerable amount of human capital (in terms of available scientists and engineers) and reasonable access to the latest technologies available, lack the capacity to absorb technology and innovate, resulting in the loss of human capital as a consequence of their structural (technological) underdevelopment. 5.2. Consequences for the Europe 2020 strategy The Europe 2020 strategy was adopted by the European Council in 2010 and represents the agenda of the European Union regarding economic growth and employment during 20102020. It concentrates on sustainable and inclusive growth to overcome the structural weaknesses of the European economy and improve its competitiveness and productivity (European Commission, 2015). The 2020 headline targets are monitored by Eurostat using nine indicators, whose current position (in green) in relation to the 2020 key targets (in red) is presented in Figure 12. Insert Figure 12 Here Figure 12 illustrates how the developments achieved fall short in the indicators that can be considered to follow directly from the structural conditions of the country: R&D expenditure and intensity [target: 3% of GDP to be invested in the research and development (R&D) sector] and employment absorption by the productive system [target: 75% of the population aged 20 to 64 years to be employed]. Note, that this is the case despite the attainments obtained in the human capital indicators, i.e. the increment in tertiary education

25

and the reduction in early leaves from education and training. That is, the structural problems prevail despite the availability of skilled labor, with migration acting as a dispersion mechanism. 5.2.1. Structural policies Our theoretical model has been designed to emphasize the interaction required between human and physical capital to generate economic growth. The model has illustrated how the resources dedicated to R&D activities may decrease among leaders, while laggards react to negative shocks to their systems to prevent the potential stagnation of their economies. However, these latter countries lack the technological infrastructure required to innovate and generate economic growth. Due to this fact, a direct transfer of technology across countries would be insufficient to foster the required response. That is, the infrastructure required by the laggards to develop their innovation systems should be the result of cooperation at the European level. The European Commission has already considered the development of industrial clusters aimed at enhancing cooperation among firms and improving the technological infrastructure of the laggards. This policy objective was highlighted in the years previous to the crisis of 2008. From a structural perspective, our results indicate that such a cooperation strategy was the correct one. However, as the data illustrates, countries have discontinued its application to focus on the immediate consequences derived from the crisis. Assume that the different Innobarometers issued by the European Commission reflect the main policy objectives of the European Union through the years. The following policy recommendations can be suggested based on our results: 

Cluster design and development: The 2006 Innobarometer (European Commission 2006) emphasized the fundamental role of a common European approach in the development of cooperative clusters used to transfer knowledge and improve the technological infrastructure of laggard countries. In this regard, Malik and Cunningham (2006) highlighted the lack of cohesion among European countries in technological and innovation policy terms - a trend that is being partially corrected in the latter years (Izsak et al., 2015).



Innovation Transfer: The 2007 Innobarometer (European Commission 2007) emphasized the importance for innovation and economic growth of both: o knowledge transfer between firms (pg. 29), and o a coherent policy to support innovation across firms and countries (pg. 40).

26

The report also highlighted the heterogeneity and lack of cohesion of the support policies implemented by different countries. The asymmetric effect of the crisis has exacerbated these frictions. In particular, the persistent gap in the SII indicator and the dispersion between both groups of countries described by the ΔAVGDP variable reflect the absence of a coherent innovation policy successfully implemented at the European level. 

Public support is important but cooperation between firms is essential: The 2010, 2012 and 2014 Innobarometers (European Commission 2010, 2012, 2014b) have focused on the importance of the public sector in supporting innovation. However, public support is insufficient if firms do not define cooperative innovation strategies between them. The struggle to achieve the Europe 2020 structural objectives despite the continuous support displayed at the public level reinforces the importance of this point.

5.2.2. Firm-level policies The innovation constraint faced by the European laggards is a formal version of what is commonly known as the middle income trap (Vivarelli, 2014a; Ozturk, 2016). The related literature suggests local innovative entrepreneurship as a means to foster innovation and structural change among the laggards, while also considering the role played by the international transference of technology as a complement of domestic innovation (Vivarelli, 2014a). The main policy recommendations that can be made at the firm level based on the findings of our model follow from Figures 1 to 5. As already stated, we have used the migratory flows to modify both the productivity of the manufacturing activities in a country and its capacity to innovate, i.e. the arrival probability of an innovation. That is, emigration has been used to reflect the structural evolution of a country. In this regard, the economic literature has already highlighted the relation between migration and growth, as well as the negative effects resulting from the brain drain experienced by the sending countries, particularly the least developed ones (Docquier, 2013; Docquier et al., 2014). Therefore, the coordination and integration among firms belonging to both types of countries is essential. The employment guidance defined within the Europe 2020 strategy concentrates on investing in skills and the creation of a frictionless and more integrated labor market to try to smooth the existing structural mismatches between labor supply and demand (European Commission, 2014a). A coordinated cooperative strategy complementing the research line defined by the European Union framework programme for research and innovation (Horizon 2020) would increase the probability of innovation among the laggard firms and the value of innovation among the leaders. Both types of countries can benefit from 27

a cooperative innovation policy that consists of sharing not only labor but also technology and the resulting value incentives from innovation. There is plenty of empirical evidence illustrating the innovation benefits that result from sharing knowledge and R&D among highly integrated firms located in countries with similar institutional frameworks and compatible technological bases (Wu and Wu, 2014; Zheng et al., 2016; Choi and Yeniyurt, 2015). Given the fact that cooperating and sharing objectives are mutually beneficial for firms and their respective countries, governments within the European Union should encourage this type of partnership to promote innovation and growth among firms and countries. This policy would allow leaders to compensate for their relatively smaller value gains while laggards would increase their probability of innovation. 6. Conclusion The formal results that follow from the model introduced in the paper provide a highly intuitive explanation for the technological and migratory patterns currently observed within and between European laggards and innovation leaders. It should be noted that we are aware of the multiple variables affecting and determining the behavior of both these patterns but do not want to impose any exogenous causality between them. Nonetheless, the model allows for a much wider equilibrium perspective than basic causality when analyzing the relation between both patterns in terms of the dynamic evolution of countries. That is, given the widening differences in technological knowledge assimilation (Alvarez et al., 2016), the existing divergences between laggard and innovator countries in terms of migration may easily be interpreted as the main [and only] compensatory mechanism available. This adjustment mechanism should compensate, to some extent, for the economic and structural asymmetries existing within the heterogeneous set of countries composing the common market [and, except for Denmark and Sweden, currency] area, see Mundell (1961) and the subsequent literature on optimal currency areas and their stability (Fingleton et al., 2015). Mainly, migration helps correcting asymmetries in unemployment rates across countries, which, in our model translates into the laggards being able to equate wages with the leaders. However, as shown by our model, shifting labor among countries constitutes only a temporal relief for the laggard economies, which remain constrained by their structural deficiencies. At the same time, skilled emigration accentuates the structural deficiencies faced by the laggards, whose absorptive capacities and innovation probabilities are considerably reduced. 28

It should be emphasized that the results obtained correspond to the most convergence enhancing scenario that may be assumed within the framework of the model. Clearly, developing an innovation does not necessarily guarantee immediate convergence in technological development levels (TDLs). For instance, assuming lower innovation value gains may easily exacerbate the stagnant trap described in the proposed framework. Similar results would follow from relaxing any of the convergence enhancing assumptions imposed through the paper. In the same way, when considering national policy implications, government policies may trigger further divergences among regions if they favor the development of infrastructures within the most developed region. That is, for a given innovation probability, political incentives may be assumed to depend on the size of the value gain differential: if it is large enough and catching up is immediate, resources may be allocated to the laggard region, but if the improvement of the NIS taking place as the result of an innovation is relatively small and catching up follows a cumulative process, then resources would be allocated to develop further the innovative [more developed] regions.

29

References [1] Abhyankar, R. (2014). The government of India's role in promoting innovation through policy initiatives for entrepreneurship development,

Technology Innovation

Management Review 4, 11-17. [2] Acemoglu, D. Introduction to Modern Economic Growth. Princeton University Press, 2008. [3] Aghion, P. and P. Howitt. (1992). A model of growth through creative destruction, Econometrica 60, 323-51. [4] Aghion, P. and P. Howitt. Growth with quality-improving innovations: An integrated framework. In: Aghion, P. and S. Durlauf (Eds.), Handbook of Economic Growth. Elsevier, North-Holland, 2005. [5] Aghion, P. and P. Howitt. Endogenous Growth Theory. Cambridge: MIT Press, 1999. [6] Alvarez, I., Di Caprio, D. and F.J. Santos Arteaga. (2016). Technological assimilation and divergence in times of crisis, Technological and Economic Development of Economy 22, 254-273. doi: 10.3846/20294913.2015.1033663 [7] Amendola, M., and J.L. Gaffard. The Innovative Choice. Oxford: Basil Blackwell, 1988. [8] Antonucci, T. and M. Pianta. (2002). Employment effects of product and process innovation in Europe, International Review of Applied Economics 3, 295-307. [9] Arcalean, C., Glomm, G. and I. Schiopu. (2012). Growth effects of spatial redistribution policies, Journal Of Economic Dynamics & Control 36, 988-1008. [10] Ballot, G. and E. Taymaz. (1997). The dynamics of firms in a micro-to-macro model: The role of training, learning and innovation, Journal of Evolutionary Economics 7, 435-457. [11] Bartels, F.L., Voss, H., Lederer, S. and C. Bachtrog. (2012). Determinants of National Innovation Systems: Policy implications for developing countries, Innovation: Management, Policy & Practice 14, 2-18. [12] Bogliacino, F., Lucchese, M. and M. Pianta. (2013). Job creation in business services: Innovation, demand, and polarization, Structural Change and Economic Dynamics 25, 95-109. [13] Borrás, S. and C. Edquist. (2013). The choice of innovation policy instruments, Technological Forecasting and Social Change 80, 1513-1522. [14] Borsi, M.T. and N. Metiu. (2015). The evolution of economic convergence in the European Union, Empirical Economics 48, 657-681. [15] Bosetti, V., Cattaneo, C. and E. Verdolini. (2015). Migration of skilled workers and 30

innovation: A European Perspective, Journal of International Economics 96, 311-322. [16] Castellacci, F. and J.M. Natera. (2016). Innovation, absorptive capacity and growth heterogeneity: Development paths in Latin America 1970–2010, Structural Change and Economic Dynamics 37, 27-42. [17] Castellacci, F. and J.M. Natera. The convergence paradox: The global evolution of national innovation systems. In: Archibugi, D. and A. Filippetti. (2015). The Handbook of Global Science, Technology, and Innovation. John Wiley & Sons. [18] Castellacci, F. and J.M. Natera. (2013). The dynamics of national innovation systems: A panel cointegration analysis of the coevolution between innovative capability and absorptive capacity, Research Policy 42, 579-594. [19] Chen, C.P., Hu, J.L. and C.H. Yang. (2011). An international comparison of R&D efficiency of multiple innovative outputs: The role of the national innovation system, Innovation: Management, Policy & Practice 13, 341-360. [20] Choi, J. and S. Yeniyurt. (2015). Contingency distance factors and international research and development (R&D), marketing, and manufacturing alliance formations, International Business Review 24, 1061-1071. [21] Cohen, W., and D. Levinthal. (1989). Innovation and learning: The two faces of R&D, Economic Journal 99, 569-596. [22] De Simone, G. and M. Manchin. (2012). Outward migration and inward FDI: Factor mobility between Eastern and Western Europe, Review Of International Economics 20, 600-615. [23] Di Caprio, D., Santos Arteaga, F.J. and M Tavana. (2015). Technology development through knowledge assimilation and innovation: A European perspective, Journal of Global Information Management 23, 48-93. [24] Docquier, F. (2013). Cross-border migration, employment and economic growth. High Level Panel on the Post-2015 Development Agenda. United Nations. http://www.post2015hlp.org/wp-content/uploads/2013/05/Docquier_Cross-BorderMigration-Employment-and-Economic-Growth.pdf [25] Docquier, F., Ozden, C. and G. Peri. (2014). The labour market effects of immigration and emigration in OECD countries, The Economic Journal 124, 1106-1145. [26] Docquier, F., and H. Rapoport. (2012). Globalization, Brain Drain, and Development, Journal of Economic Literature 50, 681-730. [27] Engel, C. and M. Kleine. (2015). Who is afraid of pirates? An experiment on the deterrence of innovation by imitation, Research Policy 44, 20-33. 31

[28] European Commission (2015). Europe 2020 strategy in a nutshell. http://ec.europa.eu/eurostat/c/portal/layout?p_l_id=6589552&p_v_l_s_g_id=0 Accessed October 24, 2015. [29] European Commission (2014a). Draft thematic guidance fiche for desk officers. Thematic objective 8: Employment and labour mobility. Version 2–27/01/2014 http://ec.europa.eu/regional_policy/sources/docgener/informat/2014/guidance_employ ment_labour_mobility.pdf [30] European Commission (2014b). Innobarometer 2014: The role of public support in the commercialisation of innovations. Flash EB Series #394. [31] European Commission (2013). Basic figures on the EU - Summer 2013 edition. http://epp.eurostat.ec.europa.eu/cache/ITY$\_$OFFPUB/KS-GL-13-002/EN/KS-GL13-002-EN.PDF [32] European Commission (2012). Innobarometer 2012: Innovation in the public sector: Its perception in and impact on business. Flash EB Series #343. [33]

European

Commission

(2010).

Innobarometer

2010:

Innovation

in

public

administration. Flash EB Series #305. [34] European Commission (2007). Innobarometer 2007: Innovation transfer. Flash EB Series #215. [35] European Commission (2006). Innobarometer 2006: Cluster’s role in facilitating innovation in Europe. Flash EB Series #187. [36] Fagerberg, J., Verspagen, B. and M. Caniels. (1997). Technology, growth and unemployment across European regions, Regional Studies 31, 457-466. [37] Fagerberg, J., Srholec, M., Knell, M., (2007). The competitiveness of nations: Why some countries prosper while others fall behind, World Development 35, 1595-1620. [38] Filippetti, A. and D. Archibugi. (2011). Innovation in times of crisis: National systems of innovation, structure, and demand, Research Policy 40, 179-192. [39] Fingleton, B., Garretsen, H. and R. Martin. (2015). Shocking aspects of monetary union: The vulnerability of regions in Euroland, Journal of Economic Geography 15, 907934. [40] Forbes, N. and D. Wield. (2008). Innovation dynamics in catch-up firms: Process, product and proprietary capabilities for development, Industry & Innovation 15, 6992. [41] Furman, J., Porter, M. and S. Stern. (2002). The Determinants of National Innovative

32

Capacity, Research Policy 31, 899-933. [42] Gerschenkron, A. Economic backwardness in historical perspective. In: Hoselitz, B. (Ed.), The Progress of Underdeveloped Areas. University of Chicago Press, 1952. [43] Giménez, G., Sanaú, J., (2007). Interrelationship among institutional infrastructure, technological innovation and growth. An empirical evidence, Applied Economics 39, 1267-1282. [44] Greenwood, J., Hercowitz, Z. and P. Krusell. (1997). Long-run implications of investment specific technological change, American Economic Review 87, 342-62. [45] Gropas, R. and A. Triandafyllidou. (2014). Emigrating in times of crisis. Highlights and new data from an e-survey on high-skilled emigrants from Southern Europe and Ireland. Global Governance Programme. European University Institute. http://globalgovernanceprogramme.eui.eu/wp-content/uploads/2014/03/SURVEYREPORT-Emigrating-in-times-of-crisis.pdf [46] Grossman, G. and E. Helpman. (1991). Quality Ladders in the Theory of Growth, Review of Economic Studies 58, 43-61. [47] Gupta, M.R. and B. Chakraborty. (2006). Human capital accumulation and endogenous growth in a dual economy, Hitotsubashi Journal Of Economics 47, 169-195. [48] Hanusch, H. and A. Pyka. (Eds.) Elgar Companion to Neo-Schumpeterian Economics. Edward Elgar, 2009. [49] Hardeman, S., Frenken, K., Nomaler, Ö. and A.L.J. Ter Wal. (2015). Characterizing and comparing innovation systems by different ‘modes’ of knowledge production: A proximity approach, Science and Public Policy 42, 530-548. [50] Harrison, R., Jaumandreu, J., Mairesse, J. and B. Peters. (2014). Does innovation stimulate employment? A firm-level analysis using comparable micro-data from four European countries, International Journal of Industrial Organization 35, 29-43. [51] Heitor, M., Horta, H. and J. Mendonça (2014). Developing human capital and research capacity: Science policies promoting brain gain, Technological Forecasting and Social Change 82, 6-22. [52] Herrmann, A.M. and A. Peine. (2011). When ‘national innovation system’ meet ‘varieties of capitalism’ arguments on labour qualifications: On the skill types and scientific knowledge needed for radical and incremental product innovations, Research Policy 40, 687-701. [53] Herstatt, C., Tiwari, R., Ernst, D. and S. Buse. (2008). India's national innovation system: Key elements and corporate perspectives. East-West Center Working Papers: 33

Economics Series, No. 96. [54] Howitt, P. and D. Mayer-Foulkes. (2005). R&D, implementation and stagnation: A Schumpeterian theory of convergence clubs, Journal of Money, Credit and Banking 37, 147-177. [55] Izsak, K., Markianidou, P. and S. Radošević. (2015). Convergence of national innovation policy mixes in Europe - Has it gone too far? An analysis of research and innovation policy measures in the period 2004-12, JCMS: Journal of Common Market Studies 53, 786-802. [56] Jovanovic, B. Learning and growth. In: Kreps, D. and K. Wallis (Eds.) Advances in Economics and Econometrics: Theory and Applications, Vol. 2. Cambridge University Press, 1997. [57] Kamien, M. and N. L. Schwartz. Dynamic Optimization. The Calculus of Variations and Optimal Control in Economics and Management. Elsevier, North Holland, 1981. [58] Livanis, G. and A. Lamin. (2016). Knowledge, proximity and R&D exodus, Research Policy 45, 8-26. [59] López, S.M., Molero, J., and F.J. Santos-Arteaga. (2011). Poverty traps in a frictionless world: The effects of learning and technology assimilation, Structural Change and Economic Dynamics 22, 106-115. [60] Lundvall, Bengt-Åke. (2007). National innovation systems - analytical concept and development tool, Industry & Innovation 14, 95-119. [61] Malik, K. and P. Cunningham. (2006). Transnational policy learning in Europe: Attempts to transfer innovation policy practices, Innovation: Management, Policy & Practice 8, 262-272. [62] Morano-Foadi, S. and M. Malena (Eds.) Integration for Third Country Nationals in the European Union: The Equality Challenge. Edward Elgar, 2012. [63] Mukoyama, T. (2003). Innovation, imitation and growth with cumulative technology, Journal of Monetary Economics 50, 361-380. [64] Mundell, Robert A. (1961). A theory of optimum currency areas, American Economic Review 51, 657-665. [65] Murphy, K.M. and R.H. Topel. (2016). Human capital investment, inequality and economic growth. NBER Working Paper # 21841. [66] Ozturk, A. (2016). Examining the economic growth and the middle-income trap from the perspective of the middle class, International Business Review 25, 726-738. doi:10.1016/j.ibusrev.2015.03.008 34

[67] Pargianas, C. (2016). Endogenous economic institutions and persistent income differences among high income countries, Open Economies Review 27, 139-159. [68] Parisi, M.L., Schiantarelli, F. and A. Sembenelli. (2006). Productivity, innovation and R&D: Microevidence for Italy, European Economic Review 50, 2037-2061. [69] Pianta, M. Innovation and employment. In: Fagerberg, J. (Ed.), The Oxford Handbook of Innovation, 2005. [70] Nature. (2009). Editorial: Cuba's biotech boom, Nature 457, 130. doi:10.1038/457130a. [71] Sharif, Naubahar. (2006). Emergence and development of the National Innovation Systems concept, Research Policy 35, 745-766. [72] Silva, E.G. and A.A.C. Teixeira. (2011). Does structure influence growth? A panel data econometric assessment of “relatively less developed” countries: 1979-2003, Industrial And Corporate Change 20, 457-510. [73] Singh, J. (2007). Asymmetry of knowledge spillovers between MNCs and host country firms, Journal of International Business Studies 38, 764-786. [74] Teixeira, A.A.C., Silva, E. and R. Mamede. (2014). Structural Change, Competitiveness and Industrial Policy: Painful Lessons from the European Periphery. Routledge. [75] Thorsteinsdóttir, H., Sáenz, T.W., Quach, U., Daar, A.S. and P.A. Singer. (2004). Cuba innovation

through

synergy,

Nature

Biotechnology

22,

DC19-DC24,

doi:10.1038/nbt1204supp-DC19. [76] Van Roy, V., Vertesy, D. and M. Vivarelli. (2015). Innovation and employment in patenting firms: Empirical evidence from Europe. IZA Discussion Paper No.9147. [77] Varsakelis, N. (2006). Education, political institutions and innovative activity: A crosscountry empirical investigation, Research Policy 35, 1083-1090. [78] Veugelers, R. and H. Schweiger. (2015). Innovation policies in transition countries: One size fits all? Economic Change and Restructuring, In press. doi: 10.1007/s10644-0159167-5. [79] Vivarelli, M. (2014a). Structural change and innovation as exit strategies from the middle income trap. IZA Discussion Paper No. 8148. [80] Vivarelli, M. (2014b). Innovation, employment and skills in advanced and developing countries: A survey of economic literature, Journal of Economic Issues 48, 123-154. [81] Vivarelli, M. (2013). Technology, employment and skills: An interpretative framework, Eurasian Business Review 3, 66-89. [82] Wälde, K. (1999). Optimal saving under Poisson uncertainty, Journal of Economic Theory 87, 194-217. 35

[83] Williams, D. (2011). Russia’s innovation system: Reflection on the past, present and future, International Journal of Transitions and Innovation Systems 1, 394-412. [84] Wilson, D.J. (2009). IT and beyond: The contribution of heterogeneous capital to productivity, Journal of Business and Economic Statistics 27, 52-70. [85] Wu, J. and Z. Wu. (2014). Local and international knowledge search and product innovation: The moderating role of technology boundary spanning, International Business Review 23, 542-551. [86] World Economic Forum. The Global Competitiveness Report 2013–2014: Full Data Edition. 2013. [87] Zheng, N., Wei, Y., Zhang, Y. and J. Yang. (2016). In search of strategic assets through cross-border merger and acquisitions: Evidence from Chinese multinational enterprises in developed economies, International Business Review 25, 177-186. doi:10.1016/j.ibusrev.2014.11.009

36

Appendix A: Bellman Equations A.1. Basic Theory We introduce a set of Poisson processes within the stochastic framework of the model building on Wälde (1999), who adopts the following version of Ito’s lemma. Let

z  ( z1, z2 )T be a vector-valued Poisson process consisting of two independent Poisson processes, z1 and z 2 . Let f (x)  ( f1 (x), f 2 (x))T , g (x) and  (x)  (1 (x),  2 (x))T be continuous real functions of x  ( x1, x2 ) . Note that f i , g ,  i : 2   . Let x follow d x  f (x)dt   (x)d z . Then, the differential dg (x) equals dg (x)  [ g x1 (x) f1 (x)  g x2 (x) f 2 (x)] dt 

[ g ( x1  1 (x), x2 )  g (x)] dz1  [ g ( x1, x2   2 (x))  g (x)] dz2 ..

(A.1)

At the same time, the differential generator Diff can be applied to dg (x) . Diff g (x)  g x1 (x) f1 (x)  g x2 (x) f 2 (x) 

(A.2)

[ g ( x1  1 (x), x2 )  g (x)] a1  [ g ( x1, x2   2 (x))  g (x)] a2 .

where ai dt , i  1, 2 , denotes the probability per unit of time that xi jumps with an amplitude of  i (x) , while Diff g (x) gives the expected change of g (x) per unit of time. A.2. Laggard Countries Consider the Poisson process triggering the increase in the TDL of an imitator country:





d  m   2   dz ,

(A.3)

and replace the corresponding variables in Equation (A.2) according to: x  ,

  (n |  )  f1 (x)   ,   (n |  ) 

f 2 (x)  0 , g (x)  V (x) ,



(A.4)



1 (x)   2   , a1  ( ,n) ,

a2  0 ,

in order to obtain





  (n |  )   dV     ( , n) V   ( 2   )  V   . E   V ( )    dt    (n |  ) 



(A.5)

Finally, include the expected temporal evolution of the value function in the Bellman 37

equation corresponding to this type of problems (refer to any standard optimization text, such as Section 21 in Kamien and Schwartz (1981)) and given by  dV     ,  dt 



V    max  (n |  )  E  

n

(A.6)

to obtain the final Bellman equation optimized by laggard countries based on their respective

 values: 





n





   (n |  )   ( , n) V   ( 2   )  V    .    (n |  )  

V m    max  (n |  )  V ( ) 

(A.7)

A.3. Innovator Countries Consider the Poisson processes triggering the increase in the TDL of an innovator country:





d  m   2  1 dz ,

(A.8)

and replace the corresponding variables in Equation (A.2) according to: x  ,

f1 (x)  1 , f 2 (x)  0 , g (x)  V (x) ,



(A.9)



1 (x)   2  1 , a1  ( , n) ,

a2  0 , in order to obtain [we have assumed that   1 within a given innovator country in order to simplify the presentation]:





 dV    2 E   V ( ) 1  ( ,n) V 1  (   )  V 1 .  dt 



(A.10)

As in the laggard case, we substitute the expected temporal evolution of the value function in the corresponding Bellman equation  dV     ,  dt 



(A.11)

V    max  (n |  )  E  

n

to obtain the final Bellman equation optimized by an innovator country





V n    max  (n |  )  V ( )  ( ,n)[V (2 )  V (1)] . n

38

(A.12)

1.3

(n|)=20

1.2

Skilled Labor Wages

1.1 1

(n|)=10

0.9 0.8 0.7 0.6

0

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0.9



Figure 1. Decreasing the reference innovator profits (   0.5 )

39

1

1.3 1-/1- 1.2 ln()

Skilled Labor Wages

1.1 1 0.9 0.8

1/2

0.7

1/4

0.6

0

0.1

0.2

0.3

0.4

0.5 

0.6

0.7

0.8

0.9

1

Figure 2. Wage function differentials and stagnant intervals (   0.5 ) Stagnant interval for ln( ) : [0, 0.065]  [0.640, 1], and for

40

 1 : [0, 0.130]  [0.7030, 1] 1

Figure 3. Increments in concavity value and the widening of stagnant intervals (   0.9 )

41

Figure 4. Value functions defined within the domain [0; 1]

42

Figure 5. Value gain from innovation vs. productivity gain in manufacturing

43

Figure 6. ΔGDP and ΔAVGDP for Germany (DE) and Spain (SP) over the period 2000-2013

44

Figure 7. Em/LF and R&D/LF for Germany (DE) and Spain (SP) over the period 2000-2013

45

(b) Technological laggards

(a) All countries

Figure 8. Scatterplot illustrating the relation between ΔGDP and Emig/LF

46

(b) Technological leaders

(a) All countries

Figure 9. Scatterplot illustrating the relation between ΔGDP and Emig/LF

47

Figure 10. Total number of long-term emigrants as a percentage of the labor force* *Note: Refer to http://appsso.eurostat.ec.europa.eu/nui/show.do?dataset=migr_emi1ctz&lang=en for additional information about this variable.

48

Figure 11. SII [summary innovation index]* *Note: The SII [summary innovation index] variable is calculated by the Innovation Union Scoreboard. The calculation of and additional intuition regarding the SII variable can be found at http://ec.europa.eu/growth/industry/innovation/facts-figures/scoreboards/index_en.htm?nl_id=1041.

49

Figure 12. Situation of the indicators in November 2015 relative to the Europe 2020 targets Source: http://ec.europa.eu/eurostat/c/portal/layout?p_l_id=6589552&p_v_l_s_g_id=0

50

Table 1. Several innovation-related indicators composing the global competitiveness index* Availability of Availability of Firm-level Capacity Country scientists latest technology for capacity to and engineers technologies absorption innovation retain talent Denmark 36 29 20 13 43 Finland 1 1 7 2 2 Germany 17 13 16 3 9 Sweden 10 2 1 7 10 Greece 5 67 88 117 86 Italy 29 69 112 31 117 Portugal 16 15 29 42 111 Spain 11 33 49 57 108 *Note: Data retrieved from the The Global Competitiveness Report 2013-2014: Full Data Edition. Refer to World Economic Forum (2013) for additional information regarding these variables. The indicators have been taken from the 7th (Labor market efficiency), 9th (Technological readiness) and 12th (Innovation) pillars. Country

51

Table 2. Variables analyzed in the model Variable Name GDP ΔGDP

Description [Eurostat data matrix code] (2000-2013 period except when indicated) Real Gross Domestic Product per capita. Percentage change of GDP over previous time period [nama_aux_gph] 8 8   GDP GDPi   i   i 1 i 1  GDPj   , j  1,...,8 8 8      

ΔAVGDP ΔAVGDP 

Real GDP per capita in country j - Average Real GDP per capita in all eight countries Average Real GDP per capita in all eight countries The index j refers to the country being considered.

Prod Emig LF Emig/LF #R&D #R&D/LF $R&D SII

[computed from variables in nama_aux_gph] Labour productivity per hour worked: real output (deflated GDP measured in chainlinked volumes, reference year 2005) per unit of labour input (measured by the total number of hours worked) [tsdec310] Total number of emigrants per year [migr_emi1ctz] Labor force (active population): sum of employed and unemployed persons [lfsi_act_a] Total number of emigrants per year as a percentage of the labor force [computed from variables in migr_emi1ctz and lfsi_act_a] Total R&D personnel in all sectors of performance [rd_p_persocc] Total R&D personnel in all sectors as a percentage of the labor force [computed from variables in rd_p_persocc and lfsi_act_a] Total intramural R&D expenditure in all sectors of performance: Euro per inhabitant [rd_e_gerdtot] Summary Innovation Index (2006-2013 period)

52

Table 3. Average values of the main indicators over the period 2000-2013. Country Denmark Finland Germany Sweden Greece Italy Portugal Spain

GDP Δ GDP 37643 0,39 29900 1,33 28107 1,24 33071 1,71 16838 0,71 24029 -0,24 14664 0,14 20564 0,62

Δ AVGDP 46,61 16,29 9,39 28,61 -34,26 -6,32 -42,85 -19,92

LF 2899,3 2645,9 40794,4 4800,3 4885,5 24404,5 5466,6 21416,9

Emig. Emig/LF Prod. # R&D # R&D/LF 42,990 1,483 50,8 48,962 1,687 12,937 0,489 38,2 55,624 2,103 511,241 1,259 40,6 516,809 1,266 41,880 0,869 42,1 76,935 1,589 80,494 1,633 20,0 35,332 0,723 75,004 0,306 32,2 197,405 0,807 22,171 0,408 16,0 35,682 0,653 254,437 1,111 28,9 181,757 0,840

53

$ R&D 1075,6 1119,4 764,8 1282,4 114,1 293,4 171,3 250,0

SII 0,687 0,671 0,672 0,748 0,378 0,417 0,390 0,399

Table 4. Values of the main indicators for Germany over the period 2000-2013 Indicator

Germany 2000

2001

2002

2003

2004

2005

2006

2007

2008

2009

2010

2011

2012

2013

ΔGDP

2,9

1,3

-0,2

-0,4

1,2

0,7

3,8

3,4

1,3

-4,9

4,2

3,3

0,5

0,2

ΔAVGDP

10,099

9,578

8,516

7,233

5,824

4,956

5,461

6,618

8,368

9,519

11,977

14,833

17,282

11,205

Emig/LF

1,703

1,530

1,571

1,576

1,745

1,538

1,548

1,536

1,776

0,689

0,607

0,605

0,580

0,622

Prod

37,3

38,2

38,7

39,1

39,4

39,9

41,3

42

42

40,9

41,7

42,4

42,6

42,8

#R&D/LF

1,225

1,213

1,210

1,189

1,178

1,163

1,182

1,221

1,260

1,287

1,320

1,396

1,430

1,447

$R&D

616,1

632,2

647,3

660,8

666

675,6

713

746,9

809,2

817,2

855,1

923,5

966,6

977,4

0,646

0,65

0,655

0,667

0,689

0,685

0,69

0,69

SII

54

Table 5. Values of the main indicators for Spain over the period 2000-2013 Indicator

Spain 2000

2001

2002

2003

2004

2005

2006

2007

2008

2009

2010

2011

2012

2013

ΔGDP

4,2

2,5

1,2

1,4

1,6

1,9

2,5

1,6

-0,7

-4,5

-0,5

-0,1

-1,7

-0,7

ΔAVGDP

-19,623

-18,847

-18,409

-18,260

-18,657

-18,367

-19,021

-19,853

-19,741

-18,744

-20,731

-21,148

-21,553

-25,986

0,193

0,326

0,270

0,322

0,653

1,013

1,250

1,634

1,726

1,745

1,905

2,295

Emig/LF Prod

27,3

27,3

27,4

27,6

27,7

27,9

28,1

28,5

28,7

29,4

30

30,4

31,5

32,1

#R&D/LF

0,685

0,697

0,708

0,767

0,795

0,827

0,868

0,897

0,935

0,949

0,950

0,918

0,891

0,877

$R&D

142,8

153,8

175,3

196,4

210,3

235,5

268,5

297,9

321,9

315,4

313,8

303,9

286

278,5

0,375

0,396

0,398

0,403

0,399

0,402

0,411

0,408

SII

55

Table 6. Correlation values between the main indicators for all countries Indicator Pearson Correlation Δ GDP

Δ AVGDP

Emig/LF

Prod.

# R&D/LF

$ R&D

SII

Δ GDP

Δ AVGDP

Emig/LF

Prod.

# R&D/LF

$ R&D

SII

1

,116

-,166

,066

,053

,074

,212

Sig. (2-tailed) N

111

,226 111

,097 101

,492 111

,595 103

,447 107

,095 63

Pearson Correlation

,116

1

Sig. (2-tailed) N Pearson Correlation Sig. (2-tailed) N

,226 111 -,166 ,097 101

,289** ,003 101 1

,970** ,000 111

,780** ,000 103 ,138 ,177 97

,872** ,000 107 ,152 ,131 100

,908** ,000 63 -,013 ,917 62

Pearson Correlation

,066

Sig. (2-tailed) N Pearson Correlation Sig. (2-tailed) N

,492 111 ,053 ,595 103

,754** ,000 104 1

,850** ,000 108

,877** ,000 64

,915** ,000 104

,866** ,000 61

Pearson Correlation

,074

1

Sig. (2-tailed) N

,447 107

,872** ,000 107

,965** ,000 64

Pearson Correlation Sig. (2-tailed) N

111 ,289** ,003 101 ,970** ,000 111 ,780** ,000 103

102 ,341** ,000 102 ,138 ,177 97

,341** ,000 102 1 112 ,754** ,000 104

104

,131 100

,850** ,000 108

,915** ,000 104

,212

,908**

-,013

,877**

,866**

,095 63

,000 63

,917 62

,000 64

,000 61

,152

** Correlation is significant at the 0.01 level (2-tailed).

56

108 ,965** ,000 64

1 64

Table 7. Correlation values between the main indicators for the technological leaders Indicator Δ GDP

Δ AVGDP

Emig/LF

Prod.

# R&D/LF

$ R&D

SII

Pearson Correlation Sig. (2-tailed) N Pearson Correlation Sig. (2-tailed) N Pearson Correlation Sig. (2-tailed) N Pearson Correlation Sig. (2-tailed) N Pearson Correlation Sig. (2-tailed) N Pearson Correlation Sig. (2-tailed) N Pearson Correlation Sig. (2-tailed) N

Δ GDP

Δ AVGDP

1 56 -,090 ,508 56 -,035 ,795 56 -,149 ,272 56 -,060 ,669 54 -,180 ,192 54 ,016 ,931 32

Emig/LF

-,090 ,508 56 1 56 ,361** ,006 56 ,846** ,000 56 ,106 ,446 54 ,390** ,004 54 ,376* ,034 32

-,035 ,795 56 ,361** ,006 56 1 56 ,570** ,000 56 -,607** ,000 54 -,397** ,003 54 ,012 ,946 32

Prod.

-,149 ,272 56 ,846** ,000 56 ,570** ,000 56 1 56 -,076 ,587 54 ,298* ,029 54 ,183 ,317 32

** Correlation is significant at the 0.01 level (2-tailed). * Correlation is significant at the 0.05 level (2-tailed).

57

# R&D/LF

-,060 ,669 54 ,106 ,446 54 -,607** ,000 54 -,076 ,587 54 1 54 ,597** ,000 54 -,098 ,594 32

$ R&D

-,180 ,192 54 ,390** ,004 54 -,397** ,003 54 ,298* ,029 54 ,597** ,000 54 1 54 ,615** ,000 32

SII

,016 ,931 32 ,376* ,034 32 ,012 ,946 32 ,183 ,317 32 -,098 ,594 32 ,615** ,000 32 1 32

Table 8. Correlation values between the main indicators for the technological laggards Indicator Pearson Correlation Δ GDP

$ R&D

SII

-,284

*

-,293 ,109

,486

,007

,039

45

55

49

53

31

Pearson Correlation

,020

1

-,188

,941**

,300*

,598**

,365*

Sig. (2-tailed)

,885

,217

,000

,036

,000

,043

Sig. (2-tailed)

Sig. (2-tailed) N Pearson Correlation Sig. (2-tailed) N Pearson Correlation Sig. (2-tailed) N Pearson Correlation

SII

-,379

**

,000

Pearson Correlation

$ R&D

# R&D/LF

-,096

55

N

# R&D/LF

-,538

Prod.

**

,885

Pearson Correlation

Prod.

,020

55

N Emig/LF

1

Sig. (2-tailed) N

Δ AVGDP

Δ GDP Δ AVGDP Emig/LF

Sig. (2-tailed) N

55

55

45

55

49

53

31

-,538**

-,188

1

,027

,430**

,009

-,030

,000

,217

,859

,004

,953

,877

45

45

46

46

43

46

30

-,096

,941**

,027

1

,515**

,738**

,457**

,486

,000

,859

,000

,000

,009

55

55

46

56

50

54

32

-,379**

,300*

,430**

,515**

1

,788**

,861**

,007

,036

,004

,000

,000

,000

49

49

43

50

50

50

29

-,284*

,598**

,009

,738**

,788**

1

,676**

,039

,000

,953

,000

,000

53

53

46

54

50

54

32

-,293

,365*

-,030

,457**

,861**

,676**

1

,109

,043

,877

,009

,000

,000

31

31

30

32

29

32

** Correlation is significant at the 0.01 level (2-tailed). * Correlation is significant at the 0.05 level (2-tailed).

58

,000

32

Online supplementary data appendix Indicator 2000 GDP ΔGDP LF Emig. Prod. # R&D $ R&D SII

36.500 3,2 2.835,7 43.417 48,1 37.693 730,2

Indicator GDP ΔGDP LF Emig. Prod. # R&D $ R&D SII

2001 36.600 0,3 2.867,1 43.980 47,8 39.892 799,8

2000 26.700 5,1 2.589,5 14.311 34,4 52.604 855,2

2001 27.300 2,1 2.604,8 13.153 35,1 53.424 891,5

Indicator 2000 GDP ΔGDP LF Emig. Prod. # R&D $ R&D SII

Indicator GDP ΔGDP LF Emig. Prod. # R&D $ R&D SII

Indicator GDP ΔGDP LF Emig. Prod. # R&D $ R&D SII

2002 36.700 0,1 2.854,3 43.481 48,2 42.406 863,2

26.300 2,9 39.580,1 674.038 37,3 484.734 616,1

2003 36.700 0,1 2.861,9 43.466 49,1 41.607 901,8

2002 27.700 1,6 2.609,6 12.891 35,6 55.044 929,8

2001 26.600 1,3 39.631,2 606.494 38,2 480.606 632,2

2004 37.500 2,1 2.897,9 45.017 50,5 42.687 907,2

2003 28.200 1,8 2.599,7 12.083 36,4 57.196 961,3

2002 26.600 -0,2 39.665,3 623.255 38,7 480.004 647,3

2005 38.300 2,1 2.892,1 45.869 51,4 43.499 941,3

2004 29.300 3,8 2.593,4 13.656 37,7 58.281 1.006,5

2003 26.500 -0,4 39.735,1 626.330 39,1 472.533 660,8

2004 26.800 1,2 39.968,0 697.632 39,4 470.729 666

2006 39.400 3,1 2.919,1 46.786 51,9 44.878 998,5 0,684

Denmark 2007 39.900 1,2 2.914,4 41.566 52,2 46.897 1.077,7 0,647

2008 39.300 -1,4 2.954,5 38.356 51,1 58.589 1.223,8 0,659

2005 30.000 2,6 2.620,8 12.369 38,4 57.471 1.045,3

Finland 2006 2007 31.200 32.700 4,0 4,9 2.648,0 2.674,9 12.107 12.443 39,5 40,8 58.257 56.243 1.096,2 1.183 0,63 0,672

2005 27.000 0,7 40.867,6 628.399 39,9 475.278 675,6

Germany 2006 2007 28.000 29.000 3,8 3,4 41.276,1 41.461,9 639.064 636.854 41,3 42 487.935 506.450 713 746,9 0,646 0,650

2009 36.900 -6,2 2.947,5 39.899 49,8 55.918 1.282 0,673

2008 32.700 -0,2 2.702,9 13.657 40,3 56.698 1.296,3 0,672

2008 29.300 1,3 41.559,5 737.889 42 523.505 809,2 0,655

2010 37.300 0,9 2.924,4 41.456 52,4 56.623 1.281,6 0,697

2009 29.700 -9,0 2.678,0 12.151 38,2 56.069 1.274,1 0,669

2009 27.900 -4,9 41.568,8 286.582 40,9 534.975 817,2 0,667

2011 37.500 0,7 2.924,2 41.593 52,5 57.585 1.312,7 0,696

2010 30.600 2,9 2.671,7 11.905 39,4 55.897 1.302,7 0,676

2010 29.100 4,2 41.558,6 252.456 41,7 548.723 855,1 0,689

2012 37.200 -0,7 2.907,4 43.663 52,6 58.657 1.358,5 0,713

2011 31.300 2,3 2.682,4 12.660 40 54.526 1.332,7 0,682

2011 30.000 3,3 41.185,9 249.045 42,4 575.099 923,5 0,685

2013 37.200 0,0 2.889,9 43.310 53,4 58.530 1.379,8 0,729

2012 30.900 -1,5 2.690,0 13.845 39,5 54.047 1.264,9 0,684

2012 30.200 0,5 41.350,7 240.001 42,6 591.261 966,6 0,690

2013 30.300 -1,8 2.676,2 13.893 39,7 52.972 1.231,7 0,680

2013 30.200 0,2 41.713,4 259.328 42,8 603.500 977,4 0,690

2000 29.400 4,3 4.493,5 34.091 37 : :

2001 29.700 1,0 4.588,1 32.141 37,2 72.190 1.179,8

2002 30.400 2,2 4.600,9 33.009 38,7 : :

2003 31.000 2,0 4.620,6 35.023 40,2 72.978 1.186,3

2004 32.200 3,8 4.636,3 36.586 41,5 72.459 1.161,6

2005 33.000 2,7 4.713,8 38.118 42,7 77.704 1.178,4

Sweden 2006 2007 34.300 35.100 3,7 2,6 4.765,7 4.838,4 44.908 45.418 44 44,1 78.715 75.318 1.295,5 1.273,7 0,732 0,723

2008 34.700 -1,4 4.897,7 45.294 43,3 79.549 1.341 0,737

2009 32.600 -5,8 4.908,1 39.240 42,3 76.711 1.142,8 0,742

2010 34.500 5,7 4.948,4 48.853 44 77.418 1.270,8 0,758

2011 35.200 2,2 5.016,4 51.179 44,4 77.950 1.386,6 0,764

2012 35.300 0,2 5.060,1 51.747 44,9 81.272 1.464,9 0,766

2013 35.600 0,8 5.115,5 50.715 45,5 80.957 1.507,6 0,760

2000 14.500 4,1 4.605,5 : 17,6 : :

2001 15.100 3,9 4.689,9 : 18,3 30.226 77,9

2002 15.500 3,1 4.745,2 : 18,6 : :

2003 16.400 5,6 4.813,3 : 19,5 31.849 88,9

2004 17.100 4,0 4.909,5 : 20,1 : 92,5

2005 17.400 1,9 4.937,0 : 19,8 33.603 104,2

Greece 2006 2007 18.300 18.900 5,2 3,2 4.975,8 4.982,3 : : 20,8 21,5 35.140 35.531 110 120,4 0,353 0,362

2008 18.800 -0,4 4.998,5 43.044 22,2 : 143,2 0,374

2009 18.200 -3,1 5.041,0 43.686 21,1 : 132,8 0,385

2010 17.400 -4,7 5.029,3 62.041 20,4 : 120,9 0,382

2011 16.200 -6,9 4.936,3 92.404 19,9 36.913 125,1 0,380

2012 15.100 -6,7 4.890,0 124.694 20,2 37.361 120,3 0,391

2013 : : 4.843,4 117.094 20,2 42.030 132,5 0,394

59

Indicator 2000 GDP ΔGDP LF Emig. Prod. # R&D $ R&D

24.000 3,6 23.487,8 56.601 32 150.066 218,9

2001 24.500 1,8 23.687,7 56.077 32,3 153.905 238,3

2002 24.500 0,1 23.887,0 49.383 32,1 164.023 256,2

2003 24.300 -0,8 24.104,5 62.970 31,7 161.828 258,5

2004 24.500 0,7 24.306,9 64.849 32,1 164.026 265,3

2005 24.500 0,2 24.284,3 65.029 32,4 175.248 269,5

SII

Indicator GDP ΔGDP LF Emig. Prod. # R&D $ R&D SII

Indicator GDP ΔGDP LF Emig. Prod. # R&D $ R&D

SII

2000 14.500 3,4 5.282,2 10.660 15 21.888 90,4

2001 14.700 1,3 5.381,4 9.800 15,1 22.970 100,5

2002 14.700 0,0 5.469,8 9.300 15,2 24.250 99

2003 14.400 -1,6 5.489,4 8.900 15,2 25.529 97,6

2004 14.600 1,0 5.476,8 10.680 15,4 25.629 106

2005 14.600 0,3 5.517,1 10.800 15,6 25.728 114,4

Italy 2006 2007 24.900 25.100 1,6 0,9 24.411,8 24.375,4 75.230 65.196 32,5 32,6 192.002 208.376 289,9 313,1 0,38 0,393

2008 24.700 -1,9 24.754,6 80.947 32,4 221.115 323,8 0,399

Portugal 2006 2007 14.800 15.100 1,1 2,1 5.555,0 5.588,8 12.700 26.800 15,8 16,1 30.531 35.334 151 187,3 0,314 0,365

2009 23.200 -6,1 24.605,2 80.597 31,7 226.527 325,6 0,412

2008 15.100 -0,1 5.590,1 20.357 16,1 47.882 245 0,392

2010 23.500 1,2 24.582,6 78.771 32,5 225.632 331,6 0,427

2009 14.600 -3,0 5.541,6 16.899 16,1 47.097 262,4 0,403

2011 23.500 0,1 24.659,5 82.461 32,5 228.094 333,7 0,428

2010 14.900 1,9 5.545,4 23.760 16,7 47.616 260,8 0,426

2012 22.800 -2,7 25.257,0 106.216 32,2 240.179 345,2 0,446

2011 14.700 -1,1 5.428,1 43.998 16,9 49.604 242,7 0,421

2013 22.400 -2,1 25.259,0 125.735 32,2 252.648 338,5 0,448

2012 14.300 -2,8 5.382,6 51.958 17 47.554 220,1 0,396

Spain 2000 2001 2002 2003 2004 2005 2006 2007 2008 2009 2010 2011 2012 19.200 19.700 20.000 20.200 20.600 21.000 21.500 21.800 21.700 20.700 20.600 20.600 20.200 4,2 2,5 1,2 1,4 1,6 1,9 2,5 1,6 -0,7 -4,5 -0,5 -0,1 -1,7 17.601,2 18.050,8 18.961,1 19.742,9 20.376,0 21.140,5 21.779,8 22.425,9 23.065,7 23.260,4 23.364,5 23.433,9 23.443,7 : : 36.605 64.298 55.092 68.011 142.296 227.065 288.432 380.121 403.377 409.034 446.606 27,3 27,3 27,4 27,6 27,7 27,9 28,1 28,5 28,7 29,4 30 30,4 31,5 120.618 125.750 134.258 151.487 161.933 174.773 188.978 201.108 215.676 220.777 222.022 215.079 208.831 142,8 153,8 175,3 196,4 210,3 235,5 268,5 297,9 321,9 315,4 313,8 303,9 286 0,375 0,396 0,398 0,403 0,399 0,402 0,411

60

2013 14.300 -0,5 5.284,6 53.786 17,1 47.931 221,4 0,400

2013 20.100 -0,7 23.190,0 532.303 32,1 203.302 278,5 0,408